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3 years ago

What is the solution to the inequality X+ (7 + 2x) <-3x

Mathematics

1 answer:

dolphi86 [110]3 years ago

3 0

Answer:

$x \: < \:- 1 \frac{1}{6}$

Step-by-step explanation:

The given inequality is

x+ (7 + 2x) <-3x

Expand parenthesis to get

x+ 7 + 2x <-3x

Group similar terms

x+ 2x +3x<-7

Combine similar terms

6x<-7

Divide both sides by 6

$x \: < \: - \frac{7}{6}$

Rewrite as improper fraction

$x \: < \:- 1 \frac{1}{6}$

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Calculus 2

FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

$\displaystyle \int_1^47\sqrt{\ln(x)}\, dx$

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

The trapezoidal rule is given by:

$\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)$

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

$\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}$

Therefore, the trapezoidal approximation is:

$\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)$

Evaluate:

$\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337$

The midpoint rule is given by:

$\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x$

Thus:

$\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)$

Simplify:

$\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319$

Simpson's Rule is given by:

$\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)$

So:

$\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)$

Simplify:

$\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834$

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2 years ago

For what value of c is the relation a function?

nydimaria [60]

Answer:

{ c ∣ c ≠ 2 , 12, -1, 0, c ∈ R }

Step-by-step explanation:

Considering the set

$\left\{\left(2,\:8\right),\left(12,\:3\right),\:\left(c,\:4\right),\:\left(-1,\:8\right),\:\left(0,\:3\right)\right\}$

As we know that

A function is said to be a relation if every x-value has one and only one y-value.

So, the value of c must not be equal to 2, 12, -1, 0 i.e. c ≠ 2, 12, -1, 0

Therefore,

{ c ∣ c ≠ 2 , 12, -1, 0, c ∈ R }

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2 years ago

The formula for the area, a, of a regular polygon in terms of the perimeter of the polygon, p, and the length of the apothem, a,

kotykmax [81]

The equivalent equation that can express the area of a polygon in terms of the perimeter is given by A = P/2

<h3>What is Polygon: </h3>

A closed, two-dimensional object composed of straight lines is called a polygon. Typically names of polygons are based on the polygon's number of sides Like triangles, rectangles, pentagons, etc.

<h3>Apothem of a polygon: </h3>

a line segment connecting the midpoint of a side to the center of a regular polygon is known as the Apothem of a polygon.

The area of a polygon with Apothem is given by

<h3> Area = 1/2 × perimeter × apothem </h3>

Here given that

Number of sides of Polygon = 5 sides

Let P be the perimeter

Given the length of the Apothem = a

By the given formula,

Area of the Polygon, A = (1/2) [P][a]

=> A = P/2

Therefore,

The equivalent equation that can express the area of a polygon in terms of the perimeter is given by A = P/2

Learn more about Polygons at

brainly.com/question/24464711

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9 months ago

Snowy's Snow Cones has a special bubble gum snow cone on sale. The cone is a regular snow cone that has a spherical piece of bub

Dmitrij [34]

Answer:

1 over 3 (3.14)(32)(2) − 4 over 3 (3.14)(0.53)

Step-by-step explanation:

not sure but i think this is the right answer

3 0

1 year ago

Which of these values for p and a will cause the function f(x)=Pa^x to be an exponential growth function?

Lera25 [3.4K]

Grouth is when a>1
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if a<1, it is exponetial decay

B is answer

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2 years ago

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